The present invention relates to a method for determining the amplitude and phase angle of a measuring signal corresponding to a current or a voltage on an electrical power supply network by using sampled values of the measuring signal, a model of the measuring signal containing at least a sinusoidal component being used to calculate the model amplitude and phase parameters of the measuring signal with the sampled values by applying a recursive least-squares estimation method.
A method of this type is described in an article by M. S. Sachdev and M. Nagpal xe2x80x9cA recursive least squares error algorithm for power system relaying and measurement applicationsxe2x80x9d, IEEE Trans. on Power Delivery, Vol. 6, No. 3, July 1991. In the case of this known method, sampled values are formed from a measuring signal corresponding to a current or voltage of an electrical power supply network and, via a linear least-squares estimation method, by using a sinusoidal signal model that models the measuring signal, are used to form a complex vector which specifies the amplitude and phase angle of the measuring signal. In this case, in a first step the real and imaginary part of the vector are in each case determined on their own. Then, in a second step, via a coordinate transformation, the polar coordinate representation of the complex vector, that is to say the magnitude and phase of the vector, can be determined from the real and imaginary part of the vector.
In the case of the known method, it is assumed that the frequency of the measuring signal is known. If this is not so, or if the frequency changes, then a separate method is needed in order to determine the frequency of the measuring signal. Methods are known, for example, which measure the distance of the zero transitions of the measuring signal and, on the basis of measuring this period, determine the frequency of the measuring signal; see, for example, E. Schrxc3xcfer (Editor): xe2x80x9cLexikon Mexcex2- und Automatisierungstechnikxe2x80x9d [Measurement and Automation Encyclopedia], VDI-Verlag, 1992, p. 204. Also known is a method for frequency measurement in which the measured signal to be examined is, in each case, filtered in parallel by a high-pass filter and an all-pass filter (German patent DE 42 11 946). The frequency of the measuring signal can be determined via the ratio between the amplitudes of the output signals from these two filters.
The present invention is directed toward specifying a method with which all the significant variables of the measuring signal can be determined simultaneously and quickly.
In the case of a method of the type indicated at the beginning, this object is achieved, according to the present invention, in that use is made of a model of the measuring signal containing the sinusoidal component in accordance with the relationship y=Axc2x7sin(2xcfx80ft+xcfx86), y designating an instantaneous value of the model of the measuring signal, A the amplitude, f the frequency, xcfx86 the phase angle and t the time. By using this model of the measuring signal and by using the sampled values, via a recursive nonlinear least-squares estimation method, the model frequency parameter of the measuring signal is also determined by the estimation together with the model amplitude parameter and the model phase angle parameter.
Although it is known, from the book by H. J. Hermann, xe2x80x9cDigitale Schutztechnikxe2x80x9d [Digital Protection Engineering], 1997, p.p. 110-111, to use a recursive, nonlinear least-squares estimation method in protection engineering, the book does not contain any reference to the fact that by using such an estimation method, sampled values of a measuring signal can be used to determine the amplitude, phase angle and frequency of the measuring signal in a single measured-value processing process.
A significant advantage of the method according to the present invention is, however, precisely that the sampled values of the measuring signal are used to determine the frequency, as well as the amplitude and phase angle, in a measured-value processing process. Therefore, the amplitude, phase angle and frequency of the measuring signal are associated with the same point in time.
Furthermore, the patent DE 42 05 300 C1 discloses a method with which the phase angle and the amplitude of a periodic signal can be determined via a phase-locked control loop (PLL (Phase-Locked Loop)).
The use of the model for the measuring signal y=Axc2x7sin(2xcfx80ft+xcfx86) leads to good results if the measuring signal has a purely sinusoidal waveform. If there is a DC component present in the measuring signal, a model of the measuring signal in accordance with the relationship y=Axc2x7sin(2xcfx80ft+xcfx86)+d is advantageously used, the summand d modeling the DC component of the measuring signal.
If the measuring signal is a signal whose frequency changes over time, in the case of such measuring signals without a DC component, a model of the measuring signal in accordance with the relationship   y  =      A    ·          sin      ⁡              (                              2            ⁢            π            ⁢                                          ∑                                  i                  =                  0                                n                            ⁢                              xe2x80x83                            ⁢                                                (                                                            f                                              (                        i                        )                                                              ⁢                                          t                      i                                                        )                                ⁢                t                                              +          ϕ                )            
advantageously can be used, and in the case of measuring signals with a DC component, a model of the measuring signal in accordance with the relationship   y  =            A      ·              sin        ⁡                  (                                    2              ⁢              π              ⁢                                                ∑                                      i                    =                    0                                    n                                ⁢                                  xe2x80x83                                ⁢                                                      (                                                                  f                                                  (                          i                          )                                                                    ⁢                                              t                        i                                                              )                                    ⁢                  t                                                      +            ϕ                    )                      +    d  
advantageously can be used, f(i) designating the ith time derivative of the frequency and modeling a change in the frequency over time, and various orders of the time derivative of the frequency being taken into account by selecting the variable n. In these models, in an extension of the model specified above, y=Axc2x7sin(2xcfx80ft+xcfx86), the frequency f is replaced by the expression             ∑              i        =        0            n        ⁢          (                        f                      (            i            )                          ⁢                  t          i                    )        ;
if only a 0th order derivative is taken into account, the integral expression becomes f(0) or f. These expanded models make it possible to determine frequency changes f(i) over time, in addition to the variables amplitude A, phase angle xcfx86 and frequency f.
In a further advantageous embodiment of the method according to the present invention, the values of the amplitude A, the phase angle xcfx86 and the frequency f determined by the estimation method are output as results only when the estimation error is less than a smallest permitted estimation error. This has the advantage that, in particular, the values estimated at the start of the method and afflicted by large estimation errors are not output, and therefore the large estimation errors cannot have any negative consequences for a user of the method.
Additional features and advantages of the present invention are described in, and will be apparent from, the following Detailed Description of the Invention and the Figures.